Globally, around half a million tonnes of spent nuclear fuel (SNF) will be in dry or wet storage by around 2050. Continued storage is not sustainable, and this SNF must eventually either be disposed (the open nuclear fuel cycle) or recycled (the closed fuel cycle). Many international studies have addressed the advantages and disadvantages of these options. To inform this debate, a detailed survey of the available literature related to environmental assessments of closed and open cycles has been undertaken. Environmental impacts are one of the three pillars that, alongside economic and societal impacts, must be considered for sustainable development. The aims are to provide a critical review of the open literature in order to determine what generic conclusions can be drawn from the broad base of international studies. This review covers the results of life cycle assessments and studies on waste arisings, showing how the management of spent fuels in the open and closed cycles impact the environment, including the use of natural resources, radioactive waste characteristics (heat loading, radiotoxicity and volume) and the size of the geological repository. In the framework of sustainable development, the next part of this review will consider economic impacts.